The present disclosure generally relates to systems and methods of operating an atomic force microscope (AFM) in one or more dynamic modes (DM), including without limitation, the tapping mode (TM) and the non-contact mode (NCM), as well as the peak force mode (PFM) and the contact mode (CM), with increased speed, while preserving the inherent characteristics of superior image quality and reducing the probe sample interaction force in each mode. More specifically, the present disclosure generally relates to systems and methods that take into account the variation of the mean deflection (or the deflection in the contact mode) of a probe in quantifying a sample topography, and utilizes and integrates: (i) an inner-outer feedback loop to regulate the mean cantilever deflection around the minimal level needed to maintain a stable probe-sample interaction in the corresponding imaging mode, (ii) an online iterative feedforward controller, (iii) an online optimization of the vibration amplitude ratio, and (iv) a feedback controller to the probe vibration generator that minimizes the set-point of the vibration amplitude, and to the root-mean-square (RMS) probe oscillation amplitude feedback controller.
AFMs are a type of high resolution scanning probe microscopes with resolutions in the range of fractions of a nanometer. In atomic force microscopy, a microscale cantilever with a sharp tip (probe) at its end may be used to scan the surface of a sample. When the tip is brought into proximity of a sample surface, the forces between the tip and the sample may lead to a deflection of the cantilever in accordance with Hooke's Law. Typically, the deflection of the cantilever is measured to obtain the sample's topography.
An AFM may be operated in a number of imaging modes, including contact modes (CM) (also called static modes) and a variety of dynamic modes, including without limitation, the TM, PFM, and NCM. In dynamic mode imaging, the cantilever is driven to oscillate vertically with constant amplitude of oscillation. Due to the interaction forces acting on the cantilever when the tip comes close to the surface of the sample, the amplitude of the oscillation may decrease. In conventional DM imaging, a microprocessor, a digital signal processor, or a field programmable gate array (FGPA) based system along with the underline control algorithms is typically used to control the height of the cantilever above the sample to maintain a constant oscillation amplitude (as in TM and NCM imaging) or constant peak repulsive force amplitude (as in PFM imaging) as the cantilever is scanned over the sample surface. The sample topography image in a DM microscope is produced by using the RMS displacement of the cantilever in the vertical direction, provided that the cantilever oscillation amplitude is well maintained at the desired set-point value during the scanning.
DM-imaging mode imaging typically produces better image quality and lesser sample distortion compared to the CM-imaging techniques due to the reduction in capillary force, friction and shear force, and contact pressure. However, DM-imaging speeds tend to be substantially slower because increasing the imaging speeds can lead to loss of interaction between the probe and the sample and/or dampening of the cantilever tapping vibration (particularly when the sample size is large).
As with most measuring devices, AFMs often require a trade-off between quality and acquisition speed. That is, some currently available AFMs can scan a surface with sub-angstrom resolution. These scanners are capable of scanning only relatively small sample areas, and even then, at only relatively low scan rates. For example, traditional commercial TM-imaging AFMs usually require a total scan time typically taking up to ten minutes to cover an area of several microns at high resolution (e.g., 512×512 pixels) and low probe-sample interaction force. The imaging speed of the PFM is generally similar to the imaging speed of the TM, whereas the imaging speed of the NCM is generally slower than the TM. This is primarily because TM and PFM operate in the repulsive force or the intermediate level between repulsive force and attractive force regions, while NCM operates purely in the attractive force region with the probe hovering further above the sample surface, and the probe-sample interaction force is much more sensitive to the probe-sample spacing in the attractive force region. As the probe-sample interaction force is much more sensitive to the probe-sample spacing in the attractive region, non-contact-mode imaging tends to be much slower than tapping-mode imaging. The practical limit of AFM scan speed is a result of the maximum speed at which the sample can be scanned while maintaining a probe-sample interaction force that is low enough not to damage or cause non-negligible damage to the tip and/or the sample.
Hence, there is a need for high-speed DM-imaging and/or CM-imaging technique that has a controlled interaction force and is suitable for imaging large size samples.